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The aim of this work is to thoroughly investigate Buchi automata augmentedwith spatial constraints. The input trees of such an automaton are infinitek-ary Sigma-trees, with the nodes standing for time points, and Sigmaincluding, additionally to its uses in classical k-ary Sigma-trees, thedescription of the snapshot of an n-object spatial scene of interest. Theconstraints, from an RCC8-like spatial Relation Algebra (RA) x, are used toimpose spatial constraints on objects of the spatial scene, eventually atdifferent nodes of the input trees. We show that a Buchi alternating automatonaugmented with spatial constraints can be simulated with a classical Buchinondeterministic automaton of the same type, augmented with spatialconstraints. We then provide a nondeterministic doubly depth-first polynomialspace algorithm for the emptiness problem of the latter automaton. Our mainmotivation came from another work, also submitted to this conference, whichdefines a spatio-temporalisation of the well-known family ALC(D) of descriptionlogics with a concrete domain: together, the two works provide an effectivesolution to the satisfiability problem of a concept of thespatio-temporalisation with respect to a weakly cyclic TBox.

Buchi automata augmented with spatial constraints: simulating an  alternating with a nondeterministic and deciding the emptiness problem for  the latter